Mathematical Analysis in Interdisciplinary Research

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Ioannis N. Parasidis received a Ph.D. in mathematical analysis from Kazakh State University in Kazakhstan in 1989. He worked in the Kazakh State University until 1994 and he is now a professor in the University of Thessaly in Greece. His research interests are extensions of operators, boundary value problems for differential, integro-differential and loaded equations, spectral and inverse problems, and difference equations. Efthimios Providas received a Ph.D. in numerical analysis from Brunel University in UK in 1990. He is an associate professor in the University of Thessaly in Greece. His expertise includes applied mathematics, numerical analysis, finite element methods and boundary value problems for differential, integro-differential, loaded and difference equations. Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 47 (in 2021).

Quasilinear Operator Equation at Resonance (E.A. Skachkova).- Control problem for a system of ODE with nonseparated multipoint and integral conditions (Abdullayev).- On generalized convexity and superquadracity (Abramovich).- Well-posedness of nonsmooth Lurie dynamical systems involving maximal monotone operators (D. Goeleven).- Numerical method for calculation of unsteady fluid flow egimes in hydraulic networks of complex structure (K.R. Aida-zade).- Numerical solution to inverse problems of recovering special type source of a parabolic equation (Rahimov).-. Using an Integrating Factor to Transform a Second Order BVP to a Fixed Point Problem (R. Anderson).- Volterra relatively compact perturbations of the Laplace operator (Biyarov).- Computational Aspects of the General Rodrigues Problem (Chender).- Approximation by Max-Product Operators of Kantorovich Type (G. Gal).- Variational Inequalities and General Equilibrium models (Milasi).- The strong convergence of Douglas-Rachford methods for the split feasibility problem (Dong).- Some Triple Integral Inequalities for Functions Defined on 3-Dimensional Bodies Via Gauss-Ostrogradsky Identity (Dragomir).- Optimal emergency evacuation with uncertainty (Scrimali).- On Global Hyperbolicity of Spacetimes: Some Recent Advances and Open Problems (Papadopoulos).- Spectrum Perturbations of Linear Operators in a Banach Space (Gil).- Perturbations of Operator Functions. A Survey (Gil).- Representation variety for the rank one affine group (Munoz).- A Regularized Stochastic Subgradient Projection Method for an Optimal Control Problem In a Stochastic Partial Differential Equation (A. Khan).- A survey on interpolative and hybrid contractions (Karapnar).- Identifying the Computational Problem in Applied Statistics (P. Kitsos).- Fractional Integral Operators in Linear Spaces (Kuang).- Anisotropic Elasticity and Harmonic Functions in Cartesian Geometry (P. Vafeas).- Hyers-Ulam stability of symmetric biderivations on Banach algebras(Park).- Some new classes of Higher order Strongly generalized preinvex functions (A. Noor).- Existence of global solutions and stability results for a non linear wave problem in unbounded domains (P. Papadopoulos).- Congestion control and optimal maintenance of communication networks with stochastic cost functions: a variational formulation (Raciti).- Nonlocal Problems for Hyperbolic Equations (S. Pulkina).- On the Solution of Boundary Value Problems for Loaded Ordinary Differential Equations (E. Providas).- Set-Theoretic Properties of Generalized Topologically Open Sets in Relator Spaces (Száz).- On Degenerate Boundary Conditions and Finiteness of the Spectrum of Boundary Value Problems (T. Sultanaev).- Deceptive systems of differential equations (Schechter).- Cooperative and noncooperative partial differential systems (Schechter).- Some Certain Classes of Combinatorial Numbers and Polynomials Attached to Dirichlet Characters: Their Construction by p-adic Integration and Applications to Probability Distribution Functions (Simsek).- Pathwise stability and positivity of semi-discrete approximations of the solution of nonlinear stochastic differential equations (S. Stamatiou).- A Solution of polynomial equations (N. Tsirivas).- Meir-Keeler sequential contractions and Pata fixed point results (Turinici).- Existence and stability of equilibrium points under the influence of Poynting-Robertson and Stokes drags in the restricted three-body problem (E. Perdiou).- Nearest Neighbour Forecasting Using Sparse Data Representation (Thomakos).- On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms (Rassias).- Product formulae for non-autonomous Gibbs semigroup (A. Zagrebnov).